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&mostharmonioustpairofaveisthatgivenbyapairsinwhiestringis23thelengthoftheother.Threeothersimpleratithsyieldotherfairlynigions，asaresho>
Table3.Harmoniousintervals
&obuildaharpwithstrihsdeffable3，butallofthesamethiess，tension，andmaterial，wewouldveryeasilybeabletomakesimple，reaso-soundingchordswithit—infaypairroupofsugsplayedtogetherwouldn’tsoundtoobad.
Thissystemiscalledthepentatoowasdisdepelybynumerousamusimanypartsoftheworldandisstillverypopulartoday（‘AmazingGrace’，‘MyGirl’，and‘IShottheSherifl’arewritteninit）.Theblathepianoareaseriesofpentatonicscales，soifyoupressthemrandomlyitwon’tsoundashorribleasifyoudothesamewiththewhiteones.
Evees
Althoughpeoplelikemusiy，theyalsolikeabitofdisdthepentatotootunefulandsafeforposerswhowaogetheiraudiendpushtheboundaries.Also，ffveaveisstillnotthatmany:buthowtoaddmore?Ahisquestiouriesofcarefulexperimentae，leadingffnallytoasystemcalledequaltemperament.Inthissystem，anoctaveisdividedupies，eachasemitone，oros，apart.
&htheideathatwhatmattersinmusicareratiosofhemselves，semitosaredeffermsofratios.Eachsuccessivesemito6perthigherthantheohismeansthatthehigherthezdihehigherthenoteis.
Afewposershaveexperimehmorethaesperodextranotesmayappearbriefiy，inmovinggraduallyfromohertoahisiscalledaglissando，orslide）.However，inallcultures，thenumberof‘proper’aveisalmostalwaystwelve.
Haviwelvenotes，peopleproceededtousejusteightofthemperoame）.Thereareonlyseveesinaheeighthisthesameastheffrst，justoavehigher（evenprofessionalmusiediatelyidentifyaruggletosaywhichoctaveitis）.
Thereasonwhyweuseohetwelvenotesinanoctavewasresolvedin1956byGeeMiller，apsychologist，whofouallythatourshort-termmemoryorethaems—hendiflereime.
Thereisasemitoweeesinthefullgroupoftwelve，soanygroupofseveweakeourscalewillinewhiitoo.So，wemighthavethisscale:AgapBCgapDgapEFgapG.（Asysequeesinwhicheachishigherthanthepree.）
&hatwehaveasetofseveestodeffneourseauseothernotesinapieusic.Ifwewahose‘gap’hemwithsymbolswhi‘asemitoheeinthesitohee’.
&ioethatffllstheffrstgapinourscaleaboveiscfuarlltehdereistuhbedriAvidsheadripf （rweqruititreend;fi）sourchB sfimata（lwlerriftrteanctffi）o.nNsoatrees rmefaeyrrbeedtoasmies.
Inieusicthereisusuallyatersmorethahekeyonic.Usually，thisheoneonwhigbeginsandends.IheRaieistheonesungon‘Some’and‘I’.ThewayJvuerdsyioGnairslasnaidd stioninthtehkeeffylmof， Ethfiisatis.Efiat（Eff）.Hence，her
Howisascale?Themaiionisthemoodofthepiece:ifthepat，celebratory，up-beatpiece，（s）heislikelytoajorscale.Toiecewhichislessemotionallyclearaminorkeyisusually.Theprimaryobjectivediflereweenmajorandmia（natural）majorssistsofatonic（whibeahesixnoteswhich‘fftbest’withit，itheirwavelehemaximumhesimplestpossiblewhole-ioswitheachother.Thesoundwaveshenbiregularevenpatternspossible.Iakesthepentatonidaddstwomorehesetwoheleadingnote，hasafrequendsevehatofthelowestnote.
Inanaturalmiwoofthehepentatonic，plustheleadingnote，havebeenlost（theyaredown-shiftedbyasemitoisthatthereisnsetofsimplewhole-ios，aisvaguer，moreplex，andlessplete-sounding.
Additionally，whenwehearanysungorplayedisinvariably（extheeelestruments）apasfullsetofharmonies.Majorstainallsuiestoo，butmi.Hehereisageuralness’or‘pleteness’inmajorscaleswhichislaminorones.‘AmazingGrad‘MyGirl’arebothinmajorscales，‘IShottheSherifl’ isminor.
Itusedtobe（andoallystillis）claimedthatindividualkeyshavetheirowionalqualities（inadditioioweenmajorandminor）.shavedemohisisnotso.Itislikelythatthisideaarhthereputationsoffamousoriialpieusic—imitatioobeinthesamekey，whicebecameassociatedwiththeemotionalqualityiisnottosaythatthechoiceofkeyisarbitrary:someisaredesigthenotesofaparticularkeyarephysicallyeasiertoplay.
Soundsequences
&herawmaterialsofmusipositionaresimilartheworldover，therehasbeedifleresdevelopmeernmusic，relativelyfewnotesareused，buttheyareofteher（chords）orioeachother（harmonies）.Ifwehadtojugglemorethainusipositionwouldbemoredifflparticular，polyphoaneousplayingofdiflerentmelodies—wouldbeewell-nighimpossible.Iernmusiymoreobeused，butbinatiohisdiflerenapproachfedthroughtoidesigrumearandaurallypolyphoerhesitar，onlyproduoteatatime，buteasilyvarythatnoterapidlyandsubtly.
Thediflereernandothermusicmayhavetheirihtury，whenpolyphonybegahoughtherearesomeolyphonyhasfarearlierroots）.Frompolyphboththecharacteristicallymulti-tuneapproachoftheWestaudiesofharmoodevelopit.Ithasbeehereasoexperimentswithpolyphonywasadesiretohavemen，women，andsiher.
Melodies
Playsomenotesinsequendyouhaveatueicallyamelody.Ifwefetaboutthediflerehenwhatislooselycalledtherhythmisallthatremaiivelengthsofthenotesahespeed（tempo）withwhichthewholethingisplayed，aerre，orsometimesmeasure）.Thisiseigofthewordrhythm，whichrefersohpattern.IheRaihm（teicalversion）is:‘long，long，medium，short，short，medium，medium’.
&reisihetimesigimesigheetre（‘e’）iswritten44.Thelivestheuospecifythebeat:14chets）.Theupperspeciffesthehesebeatspergroup.Iheendshowiecalledabar（soeis‘fourcrotchetbeatstothebar’）.
&theonlykimatterinmusic—theotherkindotwotonesthplaytogether.Everysoofteroughsofthetillcide，addiiora-highor-lowpressure.Theeflectisheardasalow-frequehefrequencyofwhichisthediflerehefrequemakeitup（Figure13）.
WatybladwhitethrillerfeaturingLondonpolidyou’llhearaswhehemblowshiswhistle:suchwhistlesusedtwopipesofslightlydiflereoproducetheirarrestingsousaren’talleasant:saopcalledthevoixcéleste，whitrolsasetofslightlyout-of-tunepipes.Whenplayedalonges，thebeatsproducedmakeapleasantlywaveringsound.
13.Beats.
Ialbreak
&ionalwaytoclassifymusistrumentsispartlybywhattheywereinallymadeof，herings，brass，woodwind，andmiseous（per）.Anotherwayisbywhetherached（likeapiano）orunpitched（likemaraypieusieedsrhythm，andusinganon-pitchedsourceavoidsdissohe‘melody’iishattherhythmsourcebeamusistrumeisteLully（1632–87）usedtothumpabigstitheground.Thisisnolongerfashionable，perhapspartlybecauseLullydiedfromit，havinghithimselforactedterminalgangre.Drumssoonbecameamorepopularshtheyarealsousedasasourceofthe‘actual’music.Forthisreason，whiledrumssuchasbassdrumsandsnaredrumsareuledrumsarepitched.
Mostpitstrumeheirherbystriking，plug，astrie，orothersolidanofairvibratebyprovidingitwithenergyfromlungsorbellows.Ineverycase，itisresonanceplusovertones（and，inthecaseofbells，uones，alsocalledsubharmonics）thatprovidetherequiredsound.
Thismakesitseemsimpletostructamusistrument，buttherearethreepligfactors.Theffrstisthatasuchasametalplatewillnotoawaveleslength，butalsoatwavelengthstwiceitswidthawillproduceothersoundsasittwists，too.
Theset—averyusefulplayers—isthatwhesuchasa12isstruck（orpluckedorbowed）itwillmoveiermionlybyitslengthbutalsobythepositiorikingpoipointhasnooptionbuttobeaheeringhaveobenodes，soifthestringisstrufromawillmakeafuhaian，andhehof160cTherewillbeanothersoundwithaian.Theseposidlyasthestring’svibrationshiftstowardsitsnaturalmodeofvibration，whichistohaveahedhencemakea240gthtoiveeflectisthatrepluellowersound，near-endplugaharsherone.
&ubesbehaveisimilaripe，thesimplestmotionisoneinwhichthereisfreemovementattheopenendaheree）atthed:soa12cmpipewillhaveafuha0dtheffrsta12cm（plusabitduetotheeion），hehofabout48cBut，justasinastring，thisishesththefualisdeffhepipe’slength，otherresonanceswillbeproducedagtoitswidth.Themixihefualaonesproducediflerenttimbres:iubes，thereismyinlowerharmonidthetimbreismorerounded，whilethinnerpipesarebrighter（orshriller，dependingonyourtaste）.Theffnalsiderationforimakersisthatastriwopointsmakesaveryquietsoundisverythiionoinysurroundingvolumeofair.Iurringintoamusistrument，amuchgreatervolumeofairmustbeputinmotioricguitar，thisisaplishedbyusiioringtoinduceasmallelectritinpickups（magswoundwithffnewire）.Inacousticguitarsariruments，thewoodensoundboard（top）isvibratedbythestringanditslargeareamovesmuchmoreairtharingalone.Also，atlowfrequehehollowbodiesofsustrumentsactasHelmholtzresonators.
&ristrumentsdonotaddeher，theyverttheenergyprovidedbybow，plectrum，orairblasttoana.Ihebodyoftheisthefrequencytowardsthe4kHzregion，thiswillsouethefactthatthesouuallyreducedalittlebyfriallosses.Thisloudemsfromthestrusystems，asweshallseeinChapter4.
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